Introduction to Transmission Line Impedance
Transmission lines are used to convey electrical signals between two points. The characteristic impedance of a transmission line is a key parameter that determines how signals propagate along the line and how much of the signal is reflected back when there is an impedance mismatch. Measuring the characteristic impedance accurately is critical for ensuring proper operation of high-speed digital and RF systems.
There are two main modes for signals traveling on a transmission line:
– Even mode: The currents flowing on the two conductors are equal in magnitude and in the same direction
– Odd mode: The currents flowing on the two conductors are equal in magnitude but in opposite directions
The characteristic impedance is different for even mode vs odd mode signals. This article will explain the concepts behind even and odd mode impedances, discuss techniques for measuring them, and provide some examples.
Even Mode vs Odd Mode Signals
To understand even vs odd mode, consider a pair of coupled transmission lines like a differential pair:
[Include diagram showing even mode and odd mode current flow on a pair of coupled lines]
For an even mode signal, equal currents flow in the same direction on both lines. This occurs when the same signal is applied to both lines referenced to a common ground. The electromagnetic fields from the currents on each line are oriented in the same direction.
For an odd mode signal, equal currents flow in opposite directions on each line. This results when equal but opposite polarity signals are applied to each line. The electromagnetic fields from the currents cancel in the space between the lines.
The impedance of the pair of lines is different for even vs odd mode excitation due to the different current distributions and resulting electromagnetic fields. In general:
– Even mode impedance is higher than the impedance of a single line
– Odd mode impedance is lower than the impedance of a single line
The exact even and odd mode impedances depend on the geometry of the transmission lines (conductor width, spacing between lines, distance to reference planes, dielectric constant of the board material, etc.)
Measuring Even and Odd Mode Impedances
There are a few different methods commonly used to measure even and odd mode impedances of transmission lines:
1. Time Domain Reflectometry (TDR)
TDR measurement involves sending a fast rise time pulse down the transmission line and measuring the reflections that result from impedance discontinuities. By analyzing the amplitude and timing of the reflections, the impedance profile along the length of the line can be determined.
To measure even mode impedance with TDR:
1. Connect both lines to the TDR pulse source
2. Connect both lines to the TDR oscilloscope input
3. Measure the steady-state reflected voltage level to calculate the even mode impedance
To measure odd mode impedance with TDR:
1. Connect one line to the TDR pulse source, terminate the other line
2. Connect one line to the scope input, terminate the other
3. Measure the steady-state reflected voltage to calculate odd mode impedance
Advantages of TDR:
– Provides impedance data vs. distance
– Locates impedance discontinuities
– One-port measurement possible
Disadvantages:
– Requires expensive TDR oscilloscope with fast rise time
– Steady-state impedance resolution is limited
2. Vector Network Analyzer (VNA)
A VNA measures the S-parameters of a network by sweeping a sine wave signal and measuring the reflected and transmitted signals. Converting the S-parameters to impedance allows the characteristic impedance to be determined at each frequency point across the sweep.
To measure even and odd mode impedance with a 4-port VNA:
1. Connect the four ports to the four ends of the coupled line pair
2. Measure the 4×4 S-parameter matrix
3. Convert the 4-port S-parameters to mixed mode S-parameters
4. Convert the differential and common mode S-parameters to even and odd mode impedances
Advantages of VNA:
– Provides impedance data vs. frequency
– Very accurate impedance measurements
– Differential and common mode impedance from same data
Disadvantages:
– Requires expensive 4-port VNA
– Mathematical transforms to get mode impedances
– Challenging to use for long transmission lines
3. Resonance Method
The resonance method uses a VNA to find frequencies where a half-wavelength resonance occurs in a transmission line. At the resonant frequencies, the input impedance to the line is purely real and is equal to the characteristic impedance.
To measure even mode impedance with the resonance method:
1. Connect both lines together at the far end
2. Connect a 2-port VNA to the input of the lines
3. Identify the resonant frequencies from the S11 trace
4. At each resonance, the input impedance is the even mode impedance
To measure odd mode impedance:
1. Connect the two lines to opposite ports of the VNA
2. Leave the far ends open circuited
3. Identify the resonant frequencies from the S21 trace
4. At each resonance, the input impedance is the odd mode impedance
Advantages:
– Uses standard 2-port VNA
– Simple post-processing
– Works well for long transmission lines
Disadvantages:
– Only provides data at discrete resonant frequencies
– Requires line length to be multiple of half-wavelength
– Slightly lower accuracy than direct VNA method
Example: Coupled Microstrip Line Impedances
As an example, consider a pair of coupled microstrip transmission lines on a PCB with the following parameters:
| Parameter | Value |
|---|---|
| Line width | 10 mil |
| Line spacing | 8 mil |
| Dielectric thickness | 5 mil |
| Dielectric constant | 4.0 |
| Copper thickness | 1.4 mil |
Using a 2D field solver, the calculated characteristic impedances at 1 GHz are:
| Mode | Impedance (Ω) |
|---|---|
| Even | 60.5 |
| Odd | 40.1 |
| Single | 50.0 |
Note that as expected, the even mode impedance is higher than the single line impedance while the odd mode impedance is lower.
These same impedances could be measured using the TDR, VNA, or resonance methods described earlier. The measured results would be used to validate the impedance targets were met and to identify any unexpected discontinuities in impedance along the transmission lines.
FAQ
What is the difference between even and odd mode impedance?
Even mode impedance is the impedance of two coupled transmission lines when they are driven with equal amplitude, in-phase signals. Odd mode impedance is the impedance when the lines are driven with equal amplitude, opposite phase signals. Even mode impedance is always higher than odd mode impedance for a given geometry.
Why is it important to control even and odd mode impedance?
In high-speed differential signaling, the even and odd mode impedances determine the characteristic impedance and coupling between the lines. If not carefully controlled, mismatches between the even and odd mode impedances can cause Mode Conversion, leading to signal integrity issues. Matching the even and odd mode impedances to the driver and receiver is important for minimizing reflections.
Which method is best for measuring even and odd mode impedance?
The best measurement method depends on the situation. Time domain reflectometry (TDR) is a good choice when impedance vs. distance data is needed to locate discontinuities along the line. A 4-port vector network analyzer (VNA) provides the most complete and accurate impedance vs. frequency data. The resonance method using a 2-port VNA is a simple technique well-suited for longer transmission lines.
How are even and odd mode impedances related to S-parameters?
For a pair of coupled lines, the 4-port S-parameters can be mathematically converted to mixed-mode S-parameters representing the differential and common mode responses. The differential and common mode S-parameters are then converted to odd and even mode impedances, respectively. So measuring the 4-port S-parameters allows the even and odd mode impedances to be extracted.
What are some typical even and odd mode impedance values?
Even and odd mode impedances depend on the transmission line geometry and dielectric properties. For a loosely coupled microstrip differential pair, the even mode impedance may be around 60-80 ohms while the odd mode is closer to 40-60 ohms. More tightly coupled lines will have a greater spread between even and odd mode. Typical single-ended microstrip impedance is 50 ohms. Stripline even and odd mode impedances are more tightly spaced due to the closer coupling.
Conclusion
Even and odd modes are two fundamental ways that signals propagate on coupled transmission line structures. The impedances for the two modes are generally different, with the even mode impedance being higher than the odd mode impedance. The exact values depend on the transmission line geometry.
There are several methods for measuring the even and odd mode impedances, including time domain reflectometry (TDR), vector network analysis (VNA), and the resonance method. Each approach has advantages and tradeoffs in terms of the data provided, accuracy, and complexity.
Accurately controlling the even and odd mode impedances is critical in high-speed digital and RF systems to avoid signal integrity issues from mode conversion and reflections. Simulations and measurements are used together to verify that impedances meet system requirements.
For further information on even and odd mode impedance, see references [1-3].
References
- E. Bogatin, Signal and Power Integrity – Simplified, 2nd ed. Prentice Hall, 2009.
- W. Hayward, Introduction to Radio Frequency Design. American Radio Relay League, 1994.
- H. Johnson and M. Graham, High-speed Signal Propagation: Advanced Black Magic. Prentice Hall, 2003.
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